1 code implementation • 2 May 2024 • Simon Vary, Pierre Ablin, Bin Gao, P. -A. Absil

Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP).

no code implementations • 14 Jun 2023 • Benoît Loucheur, P. -A. Absil, Michel Journée

Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation.

no code implementations • 29 Mar 2023 • Pierre Ablin, Simon Vary, Bin Gao, P. -A. Absil

Finally, our experiments demonstrate the promise of our approach to an array of machine-learning problems that involve orthogonality constraints.

2 code implementations • 7 Jan 2021 • Nguyen Thanh Son, P. -A. Absil, Bin Gao, Tatjana Stykel

We address the problem of computing the smallest symplectic eigenvalues and the corresponding eigenvectors of symmetric positive-definite matrices in the sense of Williamson's theorem.

Optimization and Control Spectral Theory 15A15, 15A18, 70G45

1 code implementation • 27 Nov 2020 • Thomas Bendokat, Ralf Zimmermann, P. -A. Absil

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems, dynamic low-rank decompositions and model reduction.

Numerical Analysis Numerical Analysis Differential Geometry 15-02, 15A16, 15A18, 15B10, 22E70, 51F25, 53C80, 53Z99

1 code implementation • 28 Aug 2020 • Yu Guan, Shuyu Dong, Bin Gao, P. -A. Absil, François Glineur

The usage of graph regularization entails benefits in the learning accuracy of LRTC, but at the same time, induces coupling graph Laplacian terms that hinder the optimization of the tensor completion model.

no code implementations • 20 Jul 2020 • P. -A. Absil, Ousmane Diao, Mouhamadou Diallo

Moreover, we observed that, when the model is trained on a suitable three-week period around the first hospitalization peak for Belgium, it forecasts the subsequent two months with mean absolute percentage error (MAPE) under 4%.

2 code implementations • 26 Jun 2020 • Bin Gao, Nguyen Thanh Son, P. -A. Absil, Tatjana Stykel

The symplectic Stiefel manifold, denoted by $\mathrm{Sp}(2p, 2n)$, is the set of linear symplectic maps between the standard symplectic spaces $\mathbb{R}^{2p}$ and $\mathbb{R}^{2n}$.

Optimization and Control Dynamical Systems

no code implementations • 27 Mar 2020 • Timothy Marrinan, P. -A. Absil, Nicolas Gillis

By scaling the objective and penalizing the information lost by the rank-$k$ minimax center, we jointly recover an optimal dimension, $k^*$, and a central subspace, $U^* \in$ Gr$(k^*, n)$ at the center of the minimum enclosing ball, that best represents the data.

1 code implementation • 17 May 2017 • C. A. Gomez Gonzalez, O. Wertz, O. Absil, V. Christiaens, D. Defrere, D. Mawet, J. Milli, P. -A. Absil, M. Van Droogenbroeck, F. Cantalloube, P. M. Hinz, A. J. Skemer, M. Karlsson, J. Surdej

We present the Vortex Image Processing (VIP) library, a python package dedicated to astronomical high-contrast imaging.

Instrumentation and Methods for Astrophysics

no code implementations • 14 Sep 2016 • V. Abrol, O. Absil, P. -A. Absil, S. Anthoine, P. Antoine, T. Arildsen, N. Bertin, F. Bleichrodt, J. Bobin, A. Bol, A. Bonnefoy, F. Caltagirone, V. Cambareri, C. Chenot, V. Crnojević, M. Daňková, K. Degraux, J. Eisert, J. M. Fadili, M. Gabrié, N. Gac, D. Giacobello, A. Gonzalez, C. A. Gomez Gonzalez, A. González, P. -Y. Gousenbourger, M. Græsbøll Christensen, R. Gribonval, S. Guérit, S. Huang, P. Irofti, L. Jacques, U. S. Kamilov, S. Kiticć, M. Kliesch, F. Krzakala, J. A. Lee, W. Liao, T. Lindstrøm Jensen, A. Manoel, H. Mansour, A. Mohammad-Djafari, A. Moshtaghpour, F. Ngolè, B. Pairet, M. Panić, G. Peyré, A. Pižurica, P. Rajmic, M. Roblin, I. Roth, A. K. Sao, P. Sharma, J. -L. Starck, E. W. Tramel, T. van Waterschoot, D. Vukobratovic, L. Wang, B. Wirth, G. Wunder, H. Zhang

The third edition of the "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) took place in Aalborg, the 4th largest city in Denmark situated beautifully in the northern part of the country, from the 24th to 26th of August 2016.

no code implementations • 2 Oct 2014 • L. Jacques, C. De Vleeschouwer, Y. Boursier, P. Sudhakar, C. De Mol, A. Pizurica, S. Anthoine, P. Vandergheynst, P. Frossard, C. Bilen, S. Kitic, N. Bertin, R. Gribonval, N. Boumal, B. Mishra, P. -A. Absil, R. Sepulchre, S. Bundervoet, C. Schretter, A. Dooms, P. Schelkens, O. Chabiron, F. Malgouyres, J. -Y. Tourneret, N. Dobigeon, P. Chainais, C. Richard, B. Cornelis, I. Daubechies, D. Dunson, M. Dankova, P. Rajmic, K. Degraux, V. Cambareri, B. Geelen, G. Lafruit, G. Setti, J. -F. Determe, J. Louveaux, F. Horlin, A. Drémeau, P. Heas, C. Herzet, V. Duval, G. Peyré, A. Fawzi, M. Davies, N. Gillis, S. A. Vavasis, C. Soussen, L. Le Magoarou, J. Liang, J. Fadili, A. Liutkus, D. Martina, S. Gigan, L. Daudet, M. Maggioni, S. Minsker, N. Strawn, C. Mory, F. Ngole, J. -L. Starck, I. Loris, S. Vaiter, M. Golbabaee, D. Vukobratovic

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions.

no code implementations • 23 Aug 2013 • Nicolas Boumal, Bamdev Mishra, P. -A. Absil, Rodolphe Sepulchre

Optimization on manifolds is a rapidly developing branch of nonlinear optimization.

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